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In music
Music

Music is an art form whose media is sound organized in time. Common elements of music are pitch , rhythm , dynamics , and the sonic qualities of timbre and texture ....
, a hexachord is a six-note segment of a scale or tone row. The term was adopted in the Middle Ages
Middle Ages

File:Karl 1 mit papst gelasius gregor1 sacramentar v karl d kahlen.jpgThe Middle Ages of European history are a period in history which lasted for roughly a millennium, commonly dated from the fall of the Roman Empire in the 5th century to the beginning of the Early Modern Period in the 16th century, marked by the division of Western Christi...
 and adapted in the twentieth-century in Milton Babbitt's
Milton Babbitt

Milton Byron Babbitt is an American composer. He is particularly noted for his pioneering Serialism, and electronic music....
 serial theory
Serialism

In music, serialism is a technique for Musical composition#A musical composition that uses Set to describe Aspect of music, and allows the Permutation of those sets....
.
le class="wikitable" style="float: right">
 The medieval hexachordal system (c = middle C
Middle C

C or Do is the first note of the fixed-Do solf?ge.In Western music, the expression "Middle C" refers to the musical note "C" located exactly between the two staff of the grand staff and near the top and bottom, respectively, of the bass voice and soprano voices....
)
Note Syllable
ee la
dd la sol
cc sol fa
bb? mi
bb? fa  
aa la mi re
g sol re ut
f fa ut  
e la mi  
d la sol re  
c sol fa ut  
b? mi  
b? fa  
a la mi re  
G sol re ut  
F fa ut  
E la mi  
D sol re  
C fa ut  
B mi  
A re  
G ut  


The Guidonian hexachord (named after its inventor, Guido of Arezzo
Guido of Arezzo

Image:Statue of Guido of Arezzo.jpgGuido of Arezzo or Guido Aretinus or Guido da Arezzo or Guido Monaco or Guido D'Arezzo was a music theorist of the Medieval music era....
) was the most basic pedagogical tool for learning new music in the European Middle Ages, and was often referenced in contemporary musical theory.






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In music
Music

Music is an art form whose media is sound organized in time. Common elements of music are pitch , rhythm , dynamics , and the sonic qualities of timbre and texture ....
, a hexachord is a six-note segment of a scale or tone row. The term was adopted in the Middle Ages
Middle Ages

File:Karl 1 mit papst gelasius gregor1 sacramentar v karl d kahlen.jpgThe Middle Ages of European history are a period in history which lasted for roughly a millennium, commonly dated from the fall of the Roman Empire in the 5th century to the beginning of the Early Modern Period in the 16th century, marked by the division of Western Christi...
 and adapted in the twentieth-century in Milton Babbitt's
Milton Babbitt

Milton Byron Babbitt is an American composer. He is particularly noted for his pioneering Serialism, and electronic music....
 serial theory
Serialism

In music, serialism is a technique for Musical composition#A musical composition that uses Set to describe Aspect of music, and allows the Permutation of those sets....
.

Middle Ages

 The medieval hexachordal system (c = middle C
Middle C

C or Do is the first note of the fixed-Do solf?ge.In Western music, the expression "Middle C" refers to the musical note "C" located exactly between the two staff of the grand staff and near the top and bottom, respectively, of the bass voice and soprano voices....
)
Note Syllable
ee la
dd la sol
cc sol fa
bb? mi
bb? fa  
aa la mi re
g sol re ut
f fa ut  
e la mi  
d la sol re  
c sol fa ut  
b? mi  
b? fa  
a la mi re  
G sol re ut  
F fa ut  
E la mi  
D sol re  
C fa ut  
B mi  
A re  
G ut  


The Guidonian hexachord (named after its inventor, Guido of Arezzo
Guido of Arezzo

Image:Statue of Guido of Arezzo.jpgGuido of Arezzo or Guido Aretinus or Guido da Arezzo or Guido Monaco or Guido D'Arezzo was a music theorist of the Medieval music era....
) was the most basic pedagogical tool for learning new music in the European Middle Ages, and was often referenced in contemporary musical theory. In each hexachord, all adjacent pitches are a whole tone apart, except for the middle two, which are separated by a semitone
Semitone

A semitone, also called a half step or a half tone,Aaron Copland, Leonard Bernstein, and others use "half tone".One source says that step is "chiefly US", and that half-tone is "chiefly N....
. These six pitches are named ut, re, mi, fa, sol, and la, with the semitone between mi and fa. These six names are derived from the first syllable of each half-line of the 8th century hymn Ut queant laxis
Ut queant laxis

Ut queant laxis or Hymnus in Ioannem is a plainchant hymn to John the Baptist written by Paulus Diaconus, the eighth century Lombards historian....
.

Each hexachord could start on G, C or F and the table to the right, reading upwards from the bottom, shows the notes in each hexachord for each of three octaves. Reading from left to right could, within certain limits, permit notes within different octaves to be distinguished from each other. Thus, C (modern c) was "C fa ut" (or "Cefaut"), c (modern c) was "C sol fa ut", and cc (modern c") was "C sol fa". Since the lowest pitch was designated by the Greek letter G (gamma, for 'g'), the pitch was known as "Gamma ut" or " Gamut
Gamut (disambiguation)

The term gamut originally referred to lowest note in the musical scale used in medieval music, and then to the entirety of the medieval musical scale....
", a term which came to designate the range of notes available, and later, a complete range of anything.

The hexachordal system also distinguished between B? (fa in the F hexachord, and known as "B molle" for 'soft B') and B? (mi in the G hexachord, and known as "B durum" for 'hard B'). Over time, the soft and hard variants of 'b' were depicted as a rounded '?' and a squared-off '?' which gradually developed into the modern flat and natural signs.

Since a single hexachord did not cover every possible note in the range of the gamut (only C-A, F-D excluding B natural, or G-E excluding B flat), singers would have to "mutate" between hexachords if the range of a sixth was exceeded or if there was an alternation between B natural and B flat. In this way the "Guidonian" system of multiple hexachords was different from modern solfege
Solfege

In music, solf?ge is a pedagogical solmization technique for the teaching of sight-singing in which each note of the score is sung to a special syllable, called a solf?ge syllable ....
, where a single set of syllables in one location suffices to name all possible pitches (including, often, chromatic pitches).

Because it included B durum, the G hexachord was called hexachordum durum; likewise, the F hexachord was called hexachordum molle. The C hexachord, containing neither B, was called hexachordum naturale.

Later changes to this system added hexachords that would accommodate chromatic pitches and a larger range.

Other usage

Milton Babbitt's serial theory extends the term hexachord to refer to a six-note segment of a twelve-tone row. Allen Forte
Allen Forte

Allen Forte is a music theory and musicologist. He was born in Portland, Oregon and fought in the Navy at the close of World War II before moving to the East Coast....
 in his The Structure of Atonal Music redefines the term hexachord to mean what other theorists (notably including Howard Hanson
Howard Hanson

Howard Harold Hanson was an United States of America composer, conducting, educator, music theorist, and ardent champion of American classical music....
 in his Harmonic Materials of Modern Music: Resources of the Tempered Scale and Carlton Gamer
Carlton Gamer

Carlton Gamer is an American composer and music theorist. He has taught at Princeton University, the University of Michigan, and Colorado College....
 in his "Some Combinational Resources of Equal-Tempered Systems") mean by the term hexad, a six-note pitch collection which is not necessarily a contiguous segment of a scale or a tone row.

See also

  • Hexatonic scale
    Hexatonic scale

    In music and music theory, a hexatonic scale is a scale with six pitch or note per octave. Famous examples include the whole tone scale, C D E F G A C; the augmentation scale, C D E G A B C; the Prometheus scale, C D E F A B C; and what some jazz theory calls the "blues scale", C E F F G B C....
  • Musica ficta
    Musica ficta

    In European music prior to about 1600, musica ficta referred to chromaticism altered pitches, not notated in the music, which were to be supplied by performers....
  • Guidonian hand
    Guidonian hand

    In Medieval music, the Guidonian hand was a mnemonic device used to assist singers in learning to sight reading. Some form of the device may have been used by Guido of Arezzo, a medieval music theory who wrote a number of treatises, including one instructing singers in sightreading....